it performed? 10. How is division proved? 11. How is multiplication proved? 12. What are integers, or whole numbers ? 13. What are fractions, or broken numbers ? 14. What is a mixed number? 15. When there is any thing left after division, what is it called, and how is it to be written? 16. How are fractions written? 17. What is the upper number called? 18. the lower number? 19. How do you multiply a fraction ? 20. To what do the numerator and the denominator of a fraction answer in division? 21. What is long division? 22. Rule? 23. When the divisor is a composite number, how may we proceed? 24. When the divisor is 10, 100, 1000, &c., how may the operation be contracted? 25. When there are ciphers at the right hand of the divisor, how may we proceed?

EXERCISES.

1. An army of 1500 men, having plundered a city, took 2625000 dollars; what was each man's share?

2. A certain number of men were concerned in the pay ment of 18950 dollars, and each man paid 25 dollars; what was the number of men?

3. If 7412 eggs be packed in 34 baskets, how many in a basket?

4. What number must I multiply by 135 that the product may be 505710?

5. Light moves with such amazing rapidity, as to pass from the sun to the earth in about the space of 8 minutes Admitting the distance, as usually computed, to be 95,000,000 miles, at what rate per minute does it travel?

6. If the product of two numbers be 704, and the multiplier be 11, what is the multiplicand?

Ans. 64 7. If the product be 704, and the multiplicand 64, what is the multiplier?

Ans. 11.

8. The divisor is 18, and the dividend 144; what is the quotient?

9. The quotient of two numbers is 8, and the dividend 144; what is the divisor?

10. A man wishes to travel 585 miles in 13 days; how far must he travel each day?

11. If a man travels 45 miles a day, in how many days will he travel 585 miles ?

12. A man sold 35 cows for 560 dollars; how much was that for each cow?

13. A man, selling his cows for 1¤ dollars each, received for all 560 dollars; how many did he sell?

14. If 12 inches make a foot, how many feet are there in 364812 inches?

15. If 364812 inches are 30401 feet, how many inches make one foot?

16. If you would divide 48750 dollars among 50 men, how many dollars would you give to each one?

17. If you distribute 48750 dollars among a number of men, in such a manner as to give to each one 975 dollars, how many men receive a share?

18. A man has 17484 pounds of tea in 186 chests; how many pounds in each chest?

19. A man would put up 17484 pounds of tea into chests containing 94 pounds each; how many chests must he have?

20. In a certain town there are 1740 inhabitants, and 12 persons in each house; how many houses are there ?—— in each house are 2 families; how many persons in each family? 21. If 2760 men can dig a certain canal in one day, how many days would it take 46 men to do the same? How many men would it take to do the work in 15 days? in 5 days? in 20 days? in 40 days? in 120 days?

22. If a carriage wheel turns round 32870 times in running from New York to Philadelphia, a distance of 95 miles, how many times does it turn in running 1 mile? Ans. 346. 23. Sixty seconds make one minute; how many minutes in 3600 seconds? - in 86400 seconds? in 604800 in 2419200 seconds?

seconds?

24. Sixty minutes make one hour; how many hours in 1440 minutes? in 10080 minutes? in 40320

in 672 hours?

25. Twenty-four hours make a day; how many days in 168 hours?

in 8766 hours? 26. How many times can I subtract forty-eight from four hundred and eighty?

27. How many times 3478 is equal to 47854 ?

28. A bushel of grain is 32 quarts; how many quarts must I dip out of a chest of grain to make one half (1) of a bushel? for one fourth (4) of a bushel? eighth (4) of a bushel?

for one

Ans. to the last, 4 quarts.

MISCELLANEOUS QUESTIONS,

Involving the Principles of the preceding Rules.

Note. The preceding rules, viz. Numeration, Addition, Subtraction, Multiplication, and Division, are called the Fundamental Rules of Arithmetic, because they are the foundation of all other rules.

1. A man bought a chaise for 218 dollars, and a horse for 142 dollars; what did they both cost?

2. If a horse and chaise cost 360 dollars, and the chaise cost 218 dollars, what is the cost of the horse? If the horse

cost 142 dollars, what is the cost of the chaise ?

3. If the sum of 2 numbers be 487, and the greater number be 348, what is the less number? If the less number be 139, what is the greater number?

4. If the minuend be 7842, and the subtrahend 3481, what is the remainder? If the remainder be 4361, and the minuend be 7842, what is the subtrahend?

¶ 23. When the minuend and the subtrahend are given, how do you find the remainder?

When the minuend and remainder are given, how do you find the subtrahend?

When the subtrahend and the remainder are given, how do you find the minuend?

When you have the sum of two numbers, and one of them given, how do you find the other?

When you have the greater of two numbers, and their difference given, how do you find the less number?

When you have the less of two numbers, and their difference given, how do you and the greater number?

5. The sum of two numbers is 48, and one of the numbers is 19; what is the other?

6. The greater of two numbers is 29, and their difference 10; what is the less number?

7. The less of two numbers is 19, and their difference is 10; what is the greater?

8. A man bought 5 pieces of cloth, at 44 dollars a picce; 974 pairs of shoes, at 3 dollars a pair; 600 pieces of calico, at 6 dollars a piece; what is the amount?

9. A man sold six cows, worth fifteen dollars each, and a yoke of oxen, for 67 dollars; in pay, he received a chaise, worth 124 dollars, and the rest in money; how much money did he receive?

10. What will be the cost of 15 pounds of butter, at 13 cents per pound?

11. How many bushels of wheat can you buy for 487 dollars, at 2 dollars per bushel?

¶ 24. When the price of one pound, one bushel, &c. of any commodity is given, how do you find the cost of any number of pounds, or bushels, &c. of that commodity? If the price of the 1 pound, &c. be in cents, in what will the whole cost be? If in dollars, what? if in shillings?

if in pence? &c.

When the cost of any given number of pounds, or bushels, &c. is given, how do you find the price of one pound or bushel, &c. In what kind of money wil the answer be?

When the cost of a number of pounds, &c. is given, and also the price of one pound, &c., how do you find the number of pounds, &c.

12. When rye is 84 cents per bushel, what will be the cost of 948 bushels? how many dollars will it be?

13. If 648 pounds of tea cost 284 dollars, (that is, 28400 cents,) what is the price of one pound?

When the factors are given, how do you find the product? When the product and one factor are given, how do you find the other factor?

When the divisor and quotient are given, how do you find the dividend?

When the dividend and quotient are given, how do you find the divisor?

14. What is the product of 754 and 25?

E*

15. What number, multiplied by 25, will produce 18850? 16. What number, multiplied by 754, will produce 18850? 17. If a man save six cents a day, how many cents would he save in a year, (365 days,)? how many in 45 years? how many dollars would it be? how many cows could he buy with the money, at 12 dollars each?

Ans. to the last, 82 cows, and 1 dollar 50 cents remainder.

18. A boy bought a number of apples; he gave away ten of them to his companions, and afterwards bought thirty-four more, and divided one half of what he then had among four companions, who received 8 apples each; how many apples did the boy first buy?

Let the pupil take the last number of apples, 8, and reverse the process. Ans. 40 apples.

19. There is a certain number, to which, if 4 be added, and 7 be subtracted, and the difference be multiplied by 8, and the product divided by 3, the quotient will be 64; what is that number? Ans. 27.

20. A chess board has 8 rows of 8 squares each; how many squares on the board ?

T 25. 21. There is a spot of ground 5 rods long, and 3 rods wide; how many square rods does it contain ?

D

A

C

B

Note. A square rod is a square (like one of those in the annexed figure) measuring a rod on each side. By an inspection of the figure, it will be seen, that there are as many squares in a row as rods on one side, and that the number of rows

is equal to the number of rods on the other side; therefore, 5 X 3: 15, the number of squares.

Ans. 15 square rods.

A figure like A, B, C, D, having its opposite sides equal and parallel, is called a parallelogram or oblong.

22. There is an oblong field, 40 rods long, and 24 rods wide; how many square rods does it contain?

23. How many square inches in a board 12 inches long, and 12 inches broad?

Ans. 144.